A car body typically has a rear deck member which extends in a direction of the width of the car body. The rear deck member usually supports the lower edge of a rear window glass element. Both lateral ends of the rear deck member are connected or welded to suspension towers, which receive and mount struts of rear suspensions, so as to increase the rigidity of the rear part of the car body. However, in certain rear deck structures, such as that disclosed in, for example, Japanese Unexamined Utility Model publication No. 61-117066, entitled "Rear Body Structure of a Passenger Car," laid open on July 24, 1986, the rear deck member is attached to the uppermost surface of the suspension tower and, accordingly, is subjected to vertical forces from the strut. Such a connecting structure results in insufficient connecting rigidity between the rear deck member and the suspension tower.